Use of Electrodes and Multi-Frequency Focusing to Correct Eccentricity and Misalignment Effects on Transversal Induction Measurements

ABSTRACT

A multicomponent induction logging tool uses a nonconducting mandrel. A central conducting member including wires that electrically connect at least one of the antennas to another of the antennas. Electrodes disposed about the transmitter antenna form a conductive path through a borehole fluid to the central conducting member.

CROSS-REFERENCES TO RELATED APPLICATIONS

This application is a continuation-in-part of U.S. patent applicationSer. No. 11/598,305 of Wang et al, filed on Nov. 13, 2006.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The invention is related generally to the use of multi-componentresistivity measurements for determination of properties of earthformations. In particular, the present invention discusses a method ofreducing the non-formation parasite effects in multi-componentresistivity measurements.

2. Background of the Art

Electromagnetic induction resistivity well logging instruments are wellknown in the art. Electromagnetic induction resistivity well logginginstruments are used to determine the electrical conductivity, and itsconverse, resistivity, of earth formations penetrated by a borehole.Formation conductivity has been determined based on results of measuringthe magnetic field of eddy currents that the instrument induces in theformation adjoining the borehole. The electrical conductivity is usedfor, among other reasons, inferring the fluid content of the earthformations. Typically, lower conductivity (higher resistivity) isassociated with hydrocarbon-bearing earth formations. The physicalprinciples of electromagnetic induction well logging are well described,for example, in, J. H. Moran and K. S. Kunz, Basic Theory of InductionLogging and Application to Study of Two-Coil Sondes, Geophysics, vol.27, No. 6, part 1, pp. 829-858, Society of Exploration Geophysicists,December 1962. Many improvements and modifications to electromagneticinduction resistivity instruments described in the Moran and Kunzreference, supra, have been devised, some of which are described, forexample, in U.S. Pat. No. 4,837,517 to Barber, in U.S. Pat. No.5,157,605 to Chandler et al., and in U.S. Pat. No. 5,600,246 to Faniniet al.

Conventional induction well logging techniques employ a metal pipeinside a coil mandrel. One or more transmitter coils are energized by analternating current. The oscillating magnetic field produced by thisarrangement results in the induction of currents in the formations whichare nearly proportional to the conductivity of the formations. Thesecurrents, in turn, contribute to the voltage induced in one or morereceiver coils. By selecting only the voltage component which is inphase with the transmitter current, a signal is obtained that isapproximately proportional to the formation conductivity. In aconventional induction logging apparatus, the basic transmitter coil andreceiver coil have axes which are aligned with the longitudinal axis ofthe well logging device. (For simplicity of explanation, it will beassumed that the borehole axis is aligned with the axis of the loggingdevice, and that these are both in the vertical direction. Also singlecoils will subsequently be referred to without regard for focusing coilsor the like.) This arrangement tends to induce secondary current loopsin the formations that are concentric with the vertically orientedtransmitting and receiving coils. The resultant conductivitymeasurements are indicative of the horizontal conductivity (orresistivity) of the surrounding formations. There are, however, variousformations encountered in well logging which have a conductivity that isanisotropic. Anisotropy results from the manner in which formation bedswere deposited by nature. For example, “uniaxial anisotropy” ischaracterized by a difference between the horizontal conductivity, in aplane parallel to the bedding plane, and the vertical conductivity, in adirection that is commonly perpendicular to the bedding plane. Whenthere is no bedding dip, horizontal resistivity can be considered to bein the plane perpendicular to the borehole, and the vertical resistivityin the direction parallel to the borehole. Conventional inductionlogging devices, which tend to be sensitive only to the horizontalconductivity of the formations, do not provide a measure of verticalconductivity or of anisotropy. Techniques have been developed todetermine formation anisotropy. See, e.g. U.S. Pat. No. 4,302,722 toGianzero et al. Transverse anisotropy often occurs such that variationsin resistivity occur in the azimuthal direction.

Multi-component signals can be used for interpreting formationresistivities and petrophysical parameters. The principles used for thisinterpretation have been discussed, for example, in U.S. Pat. No.6,470,274 to Mollison et al., U.S. Pat. No. 6,643,589 to Zhang et al.,U.S. Pat. No. 6,636,045 to Tabarovsky et al., the contents of which areincorporated herein by reference. Specifically, the parameters estimatedmay include horizontal and vertical resistivities (or conductivities),relative dip angles, strike angles, sand and shale content and watersaturation. In addition, U.S. patent application Ser. No. 11/125,530 ofRabinovich et al. teaches the use of multi-component measurements foranalysis of fractured earth formations that may also have anisotropiclayers. These multi-component signals are typically obtained using amulti-component measurement tool having coils oriented transverse to thetool axis in addition to coils oriented parallel to the tool axis.

In addition to formation response, resistivity measurements can beaffected by magnetic fields that arise from non-formation effects. Twosuch non-formation effects result from tool eccentricity within theborehole and coil misalignment with respect to the tool axis. Inductiontools generally give rise to a current flow in the conductive drillingmud that surrounds the tool and fills the borehole. Tool eccentricitygenerally causes more problems to transverse (X or Y) coils than toaxial (Z) coils. FIGS. 3A-C show cross-sectional views of an inductiontool having a non-conductive mandrel at different positions within aborehole. FIG. 3A shows an x-oriented tool 304 that is centered withinthe borehole 302 filled with mud 306. In one aspect, the current inducedin the borehole generally flows along the axial channel 307 and in theopposite direction along the axial channel 309. Due to the symmetry ofthe current flow channels (307 and 309), the centered induction tooldoes not experience an eccentricity effect. In FIG. 3B, the tool isdecentralized along the x-direction. Due to the orientation of thetransmitter, the current flowing along channels 307 and 309 stilldisplays symmetry and thus this eccentricity generally does not affectthe measurements much. FIG. 3C shows the induction tool decentralizedalong the y-axis, such that channel 307 is constricted while the lowerchannel is broadened 309. Additionally, current flowing in channel 307may interact with the formation. Thus, the borehole current flow ishighly affected due to decentralization along the y-axis. The netborehole current induces signals in transverse receiver coils,especially coplanar transmission and receiver coils. The net current mayalso induce signals in axial receiver coils that are at different axialpositions from the transverse transmitter coil. Because the inductioncurrent density increases with increasing mud conductivity, the netcurrent-induced signals are stronger for higher mud conductivity.

The eccentricity effects may be reduced by using a conductive mandrel.However, such a conductive mandrel is highly susceptible to the effectsof coil misalignment. The coil misalignment effect is due to theposition of coils with respect to the tool axis or inner pipe. Inductiontool coils are typically disposed on a pipe which may be of a highlyconductive metal. The pipe serves several purposes, such as protectingand shielding through-wires and supporting the tool weight. A transversetransmitter coil induces an induction current in the pipe if the pipeforms a closed loop with other paths of electric current. However, thepipe current does not necessarily distort the tool measurement. If thereceiver coil, coplanar with the transmitter coil, is symmetric withrespect to the pipe axis, the measurement is typically not affected. Thepipe induction current affects the measurement only if the receiver coilalso is asymmetric with respect to the pipe axis. An orthogonaltransverse receiver coil may also be affected by coil misalignment. Inaddition to the coil misalignment error caused by the pipe eddy current,misaligned orthogonal coils will also induce direct coupling between thecoils.

U.S. patent application Ser. No. 11/598,305 of Wang et al, having thesame assignee as the present disclosure teaches the use of a conductiveouter sleeve provided with a plurality of openings on the mandrel toreduce the effect of currents flowing in the borehole fluid. Onedrawback is that the sleeve is insulated from the metal pipe, so thatthe compensation may not be effective for all values of the current inthe metal pipe. The present disclosure addresses this potentialdrawback.

SUMMARY OF THE INVENTION

One embodiment of the disclosure is an apparatus for determining aresistivity property of an earth formation. The apparatus includes alogging tool having a non-conductive mandrel, a transmitter antenna, apair of receiver antennas, a central conducting member including wiresthat electrically connect at least one of the antennas to another of theantennas, and a pair of electrodes disposed about the transmitterantenna forming a conductive path through a borehole fluid to thecentral conducting member. The transmitter antenna may have an axisinclined at a nonzero angle to an axis of the logging tool. One of thepair of receiver antennas may be a bucking antenna. The receiverantennas may have axes inclined at a nonzero angle to an axis of thelogging tool. The apparatus may include a conveyance device configuredto convey the logging tool into a borehole in the earth formation, theconveyance device selected from (i) a wireline, and (ii) a drillingtubular. The apparatus may further include a processor configured toactivate the transmitter antenna at a plurality of frequencies, performa multifrequency focusing (MFF) of signals received by the receiverantennas, and determine the resistivity property of the earth formationfrom the results of the MFF.

Another embodiment is a method of determining a resistivity property ofan earth formation. The method includes conveying a logging tool havinga non-conductive mandrel, a transmitter antenna, a pair of receiverantennas and a central conducting member including wires that connect atleast one of the antennas to another of the antennas, into a borehole;positioning a pair of electrodes about the transmitter antenna andforming a conductive path through a borehole fluid to the centralconducting member; activating the transmitter antenna; producing signalsin the pair of receiver antennas responsive to the activation of thetransmitter antenna; and determining the property of the earth formationfrom the produced signals. The method may include using for thetransmitter antenna, an antenna with an axis inclined at a nonzero angleto an axis of the logging tool. The method may include using one of thepair of receiver antennas as a bucking antenna. The method may includeusing, as the receiver antennas, antennas with axes inclined at anonzero angle to an axis of the logging tool. The method may includeconveying the logging tool into a borehole in the earth formation usinga conveyance device selected from (i) a wireline, and (ii) a drillingtubular. Determining the property may be done by operating thetransmitter antenna at a plurality of frequencies; performing amultifrequency focusing (MFF) of signals received by the receiverantennas; and determining the resistivity property of the earthformation from the results of the MFF. The property may be a verticalresistivity, a horizontal resistivity, a sand fraction, a watersaturation, a formation dip, and/or an azimuth.

Another embodiment is a computer readable medium for use with anapparatus for determining a property of an earth formation. Theapparatus includes a logging tool having a non-conductive mandrel, atransmitter antenna; a pair of receiver antennas; a central conductingmember including wires that electrically connect at least one of theantennas to another of the antennas; and a pair of electrodes disposedabout the transmitter antenna forming a conductive path through aborehole fluid to the central conducting member. The medium includesinstructions that enable a processor to determine from signals receivedby the pair of receiver antennas resulting from activation of thetransmitter antenna the property of the earth formation. The medium maybe a ROM, an EPROM, an EEPROM, a flash memory, and/or an optical disk.

BRIEF DESCRIPTION OF THE FIGURES

The present invention is best understood with reference to the followingfigures in which like numbers refer to like components and in which:

FIG. 1 (Prior Art) illustrates an induction instrument disposed in aborehole penetrating an earth formation;

FIG. 2 (Prior Art) illustrates the arrangement of transmitter andreceiver coils in a multi-component induction logging tool marketedunder the name 3DExplorer®;

FIGS. 3A-C (Prior Art) show a cross-sectional view of an induction toolat different locations within a borehole;

FIG. 4 (Prior Art) shows an exemplary prior art multicomponent tool witha nonconductive mandrel and an internal metal pipe not connected to theborehole fluid;

FIG. 5 shows an exemplary multicomponent tool with a nonconductivemandrel and an internal metal pipe electrically connected to theborehole fluid using electrodes placed above, below, and in-betweentransmitter and receiver coils;

FIG. 6 illustrates a logging tool with only two electrodes above andbelow a transmitter suitable for multifrequency measurements andmultifrequency focusing; and

FIG. 7 shows the model used for evaluating the tool configurations ofFIGS. 4-6.

DETAILED DESCRIPTION OF THE INVENTION

Referring now to FIG. 1, an electromagnetic induction well logginginstrument 10 is shown disposed in a wellbore 2 drilled through earthformations. The earth formations are shown generally at 4. Theinstrument 10 can be lowered into and withdrawn from the wellbore 2 byuse of an armored electrical cable 6 or similar conveyance known in theart. The instrument 10 can be assembled from three subsections: anauxiliary electronics unit 14 disposed at one end of the instrument 10;a coil mandrel unit 8 attached to the auxiliary electronics unit 14; anda receiver/signal processing/telemetry electronics unit 12 attached tothe other end of the coil mandrel unit 8, this unit 12 typically beingattached to the cable 6.

The coil mandrel unit 8 includes induction transmitter and receivercoils, as will be further explained, for inducing electromagnetic fieldsin the earth formations 4 and for receiving voltage signals induced byeddy currents flowing in the earth formations 4 as a result of theelectromagnetic fields induced therein.

The auxiliary electronics unit 14 can include a signal generator andpower amplifiers (not shown) to cause alternating currents of selectedfrequencies to flow through transmitter coils in the coil mandrel unit8. A processor which controls the operation of the tool and processingacquired data may be part of the electronics unit. Alternatively, someor all of the processing and control may be done by a surface processor.

The receiver/signal processing/telemetry electronics unit 12 can includereceiver circuits (not shown) for detecting voltages induced in receivercoils in the coil mandrel unit 8, and circuits for processing thesereceived voltages (not shown) into signals representative of theconductivities of various layers, shown as 4A through 4F of the earthformations 4. As a matter of convenience the receiver/signalprocessing/telemetry electronics unit 12 can include signal telemetry totransmit the conductivity-related signals to the earth's surface alongthe cable 6 for further processing, or alternatively can store theconductivity related signals in an appropriate recording device (notshown) for processing after the instrument 10 is withdrawn from thewellbore 2.

Referring to FIG. 2, the configuration of transmitter and receiver coilsin the 3DEX® multi-component induction logging instrument of BakerHughes Incorporated is shown. This is for exemplary purposes only, andany multi-component tool may be used. Three orthogonal transmitters 101,103 and 105 that are referred to as the T_(x), T_(z), and T_(y)transmitters are shown (the z-axis is the longitudinal axis of thetool). Corresponding to the transmitters 101, 103 and 105 are associatedreceivers 107, 109 and 111, referred to as the R_(x), R_(z), and R_(y)receivers, for measuring the corresponding magnetic fields. Magneticfields induced by a transmitter are subsequently recorded at a selectedreceiver. The magnetic field is generally referred to with indicesindicating the orientation of the transmitter used and the orientationof the receiver used. Thus H_(xy), for example, indicates the responseof a field generated by the T_(x) transmitter and subsequently recordedat the R_(y) receiver. In one mode of operation of the tool, the H_(xx),H_(yy), H_(zz), H_(xy), and H_(xz) components are measured, though othercomponents may also be used. It should be noted that the method of thepresent invention may also be used with non-orthogonal configurations oftransmitters and receivers. Well known coordinate rotation methods maybe used with such non-orthogonal measurements to rotate them into thedesired orientation. For the purposes of the present invention, all suchmeasurements (orthogonal and non-orthogonal) will be referred to asmulti-component measurements.

FIG. 4 shows an exemplary multicomponent logging tool 411 having atransmitter 401 and a receiver array comprised of antennas 407 a, 407 b.One of these may be a bucking antenna and the other a measuring antenna.The conducting pipe is indicated by 403 and the insulation by 405.

FIG. 5 shows an exemplary multicomponent tool in which the tool of FIG.4 has been provided with electrodes 501 a, 501 b, 501 c, 501 d, 501 e,501 f and 501 g that couple the conducing tube 403 to the exterior ofthe tool and the borehole fluid. These electrodes are positioned aboveand below the transmitter and receiver antennas as well as in-betweenthe antennas. This has a superficial similarity to the sheet used inWang which simply acts as a Faraday shield, the arrangement of FIG. 5ensures that there will be a potential gradient in the borehole fluidthat is the same as that in the metal pipe. A third arrangementinvestigated is illustrated in FIG. 6 and only has electrodes 603, 606on either side of the transmitter antenna 601 and no electrodesproximate to the receiver antennas. Multifrequency measurements weresimulated using this tool and multifrequency focusing (MFF) was applied.

The model of the eccentered tool is illustrated in FIG. 7. The formationhas a conductivity of 60 mS/m while the borehole fluid 703 has aconductivity of 5000 mS/m. The borehole 701 has a diameter of 8 in.(20.32 cm) and the tool 705 is eccentered by a distance 707.

The results of numerical simulations for all three tool configurationsare presented in Tables 1, 2, and 3 respectively. For each configurationwe consider models without a borehole, with a borehole and a perfectlycentralized tool, and with a borehole and an eccentered tool. For thetool configurations with electrodes (Tables 2 and 3) we also consider acase with a borehole and a centralized tool when both receiver andtransmitter coils are misaligned by 1 mm from the tool axis. Since thetool without electrodes is not affected by misalignment, we do notpresent these calculations.

We can observe that the tool without electrodes (Table 1) is verysensitive to eccentricity—a single frequency response for the eccenteredcase is almost 10 times larger than for the centralized case (Ra/Rt:7.67 vs 0.795). The MFF with 3 terms can mostly compensate for it, butit requires very accurate measurements for this amount of compensation.We can see that the MFF with 4 and 5 terms start oscillating whichindicates insufficient accuracy of the data for required depth ofcompensation. It means that this approach won't work for real data withthe normal tool and measurement errors.

TABLE 1 Numerical simulation results for the tool without electrodes

The 1^(st) frequency 20.8 kHzH_(s)    H_(L)     calibrated MFF/Rt,number of terms:2   3   4   5 No borehole −4.73 e−4 −1.89 e−5 1.239 e−4(.821) 0.949 1.009 1.007 1.031 Borehole, no eccen. −7.29 e−4 −8.45 e−51.201 e−4 (.795) 0.978 1.016 1.012 1.016 Borehole, eccen. 2″  2.16 e−3 1.45 e−3 1.158 e−3 (7.67) 1.879 1.060 0.883 1.378

The tool with multiple electrodes (Table 2) shows very littlesensitivity to the eccentricity (0.759 vs 0.765) but it is stronglyaffected by very small misalignment (0.759 vs 3.34). The MFF slightlyimproves the results but not enough for practical use. Also, oscillationof the MFF results for higher number of terms indicates excessivecompensation of the signals and consequently requirements forunachievable accuracy of the measurements.

TABLE 2 Numerical simulation results for the tool with multipleelectrodes

The 1^(st) frequency 20.8 kHzH_(s)    H_(L)     calibrated MFF/Rt,number of terms:2   3   4   5 No borehole −3.11 e−4  5.77 e−5 1.239 e−4(.821) 0.946 1.005 0.995 0.947 Borehole, no eccen. −6.31 e−4 −3.06 e−51.146 e−4 (.759) 0.974 1.010 0.993 0.970 Borehole, eccen. 2′ −6.87 e−4−4.33 e−5 1.155 e−4 (.765) 1.406 1.096 0.775 0.999 Borehole, no eccen.−6.33 e−4  3.97 e−4 5.047 e−4 (3.34) 2.534 1.198 0.412 0.842 T&R_(L)misalign. 1 mm

The numerical simulation for the tool with only two electrodes (Table 3)confirms our idea for a reasonable compromise. We can see that thisconfiguration has almost no sensitivity to the tool misalignment (0.782vs 0.777) and the effect of tool eccentricity, while quite apparent forsingle frequency measurements (0.782 vs 0.614), can be easilycompensated by the MFF. The convergence of the MFF with the highernumber of terms and low single frequency signals support acceptablecompensation for the MFF transformation.

TABLE 3 Numerical simulation results for the tool with only twoelectrodes

The 1^(st) frequency 20.8 kHzH_(s)    H_(L)     calibrated MFF/Rt,number of terms:2   3   4   5 No borehole −3.72 e−4  2.37 e−5 1.237 e−4(.819) 0.949 1.011 0.998 0.984 Borehole, no eccen. −6.65 e−4 −5.31 e−51.181 e−4 (.782) 0.978 1.015 1.004 0.987 Borehole, eccen. 2″ −7.01 e−4−8.56 e−5 9.265 e−5 (.614) 0.171 1.114 1.033 0.913 Borehole, no eccen.−6.67 e−4 −5.43 e−5 1.173 e−4 (.777) 0.975 1.007 0.980 0.910 T&R_(I.)misalign. 1 mm

The invention may also be implemented in conjunction with ameasurement-while-drilling arrangement in which the multi-component andmulti-array measurements are made using a suitable device on abottomhole assembly conveyed on a drilling tubular such as adrillstring.

The measurements made by the logging tool may be used to determine aproperty of an earth formation. Methods of determination of suchproperties of the earth formation are discussed, for example, in U.S.Pat. No. 6,493,632 to Mollison et al., U.S. Pat. No. 6,470,274 toMollison et al., and U.S. Pat. No. 6,686,736 to Schoen et al., havingthe same assignee as the present invention and the contents of which areincorporated herein by reference. Such properties include vertical andhorizontal resistivities, sand fraction and water saturation. Inaddition, properties such as formation dip and azimuth may be determinedusing methods discussed in U.S. Pat. No. 6,643,589 to Zhang et al.,having the same assignee as the present invention and the contents ofwhich are incorporated herein by reference. The results of such analysisare output to a suitable medium and used for making decisions regardingreservoir development including well completion, running of other logs,and drilling of additional wells.

Implicit in the control and processing of the data is the use of acomputer program on a suitable machine readable medium that enables theprocessors to perform the control and processing. The machine readablemedium may include ROMs, EPROMs, EEPROMs, Flash Memories and Opticaldisks.

While the foregoing disclosure is directed to the preferred embodimentsof the invention, various modifications will be apparent to thoseskilled in the art. It is intended that all variations within the scopeof the appended claims be embraced by the foregoing disclosure.

1. An apparatus for determining a resistivity property of an earthformation, the apparatus comprising: (a) a logging tool having anon-conductive mandrel; (b) a transmitter antenna; (c) a pair ofreceiver antennas; (d) a central conducting member including wires thatelectrically connect at least one of the antennas to another of theantennas; and (e) a pair of electrodes disposed about the transmitterantenna forming a conductive path through a borehole fluid to thecentral conducting member.
 2. The apparatus of claim 1, wherein thetransmitter antenna further comprises an antenna with an axis inclinedat a nonzero angle to an axis of the logging tool.
 3. The apparatus ofclaim 1, wherein one of the pair of receiver antennas further comprisesa bucking antenna.
 4. The apparatus of claim 1, wherein the receiverantennas further comprise antennas with axes inclined at a nonzero angleto an axis of the logging tool.
 5. The apparatus of claim 1 furthercomprising a conveyance device configured to convey the logging toolinto a borehole in the earth formation, the conveyance device selectedfrom (i) a wireline, and (ii) a drilling tubular.
 6. The apparatus ofclaim 1 further comprising a processor configured to: (i) activate thetransmitter antenna at a plurality of frequencies; (ii) perform amultifrequency focusing (MFF) of signals received by the receiverantennas; and (iii) determine the resistivity property of the earthformation from the results of the MFF.
 7. A method of determining aresistivity property of an earth formation, the method comprising: (a)conveying a logging tool having a non-conductive mandrel, a transmitterantenna, a pair of receiver antennas and a central conducting memberincluding wires that connect at least one of the antennas to another ofthe antennas, into a borehole; (b) positioning a pair of electrodesabout the transmitter antenna and forming a conductive path through aborehole fluid to the central conducting member; (c) activating thetransmitter antenna; (d) producing signals in the pair of receiverantennas responsive to the activation of the transmitter antenna; and(e) determining the property of the earth formation from the producedsignals.
 8. The method of claim 7 further comprising, using for thetransmitter antenna, an antenna with an axis inclined at a nonzero angleto an axis of the logging tool.
 9. The method of claim 7 furthercomprising using one of the pair of receiver antennas as a buckingantenna.
 10. The method of claim 7, further comprising using, as thereceiver antennas, antennas with axes inclined at a nonzero angle to anaxis of the logging tool.
 11. The method of claim 7 further comprisingconveying the logging tool into a borehole in the earth formation usinga conveyance device selected from (i) a wireline, and (ii) a drillingtubular.
 12. The method of claim 7 wherein determining the propertyfurther comprises: (i) operating the transmitter antenna at a pluralityof frequencies; (ii) performing a multifrequency focusing (MFF) ofsignals received by the receiver antennas; and (iii) determining theresistivity property of the earth formation from the results of the MFF.13. The method of claim 7 wherein the property is selected from (i) avertical resistivity, (ii) a horizontal resistivity, (iii) a sandfraction, (iv) a water saturation, (v) a formation dip, and (vi) anazimuth.
 14. A computer readable medium for use with an apparatus fordetermining a property of an earth formation, the apparatus comprising:(a) a logging tool having a non-conductive mandrel; (b) a transmitterantenna; (c) a pair of receiver antennas; (d) a central conductingmember including wires that electrically connect at least one of theantennas to another of the antennas; and (e) a pair of electrodesdisposed about the transmitter antenna forming a conductive path througha borehole fluid to the central conducting member; the medium comprisinginstructions that enable a processor to determine from signals receivedby the pair of receiver antennas resulting from activation of thetransmitter antenna the property of the earth formation.
 16. The mediumof claim 15 further comprising at least one of (i) a ROM, (ii) an EPROM,(iii) an EEPROM, (iv) a flash memory, and (v) an optical disk.